This sort of begs the question - if your phone is shutting off suddenly at 40%, is the battery really at 40%?
People have certain preconceived expectations when they see a percentage. The best analog I can think of is a gas tank. People know that how they drive affects their fuel consumption, but they also know that when their gas tank is 40% full, their car's not going to shut off suddenly.
Perhaps we need to look at using a different measure than percent to indicate remaining battery life. Having said that, I don't know what that different measure would be.